Limits & Continuity Questions and Answers

Suppose that In 3 a and In 11 b Use properties of logarithms to write the logarithm in terms of a and b In 33 In 33 33 ww

Score 0 4 14 0 14 answered Question 1 3 Which of the following are equivalent to log 4 1 log 64 1 2 log 24 log 6 log 16 logb 10 log 40 1 logb Submit Question Question Help Message instructor

5 The function g is given by g x ln 3x 1 ln x x 6 For which values of x is g x 0

a Compute the probability of receiving six calls in a 5 minute interval of time The Poisson distribution is a discrete probability distribution used to calculate probabilities related to a random variable counting the number of times an event occurs over a specified interval The parameter u represents the mean number of times we expect the event to occur over the specified interval For a Poisson random variable where is the mean number of occurrences over a specified interval the formula for calculating the probability of x occurrences in the interval f x is given below He f x X Before the formula can be used the time intervals must be the same Since we want to find the probability of 6 calls in a 5 minute time interval but are given that the mean number of calls per hour is 36 calls per hour we must first convert the mean number of calls per hour to the mean number of calls per 5 minute time interval The following conversion factor can be used to find the mean number of calls per minute when given the mean number of calls per hour calls 1 hour hour 60 minutes Convert 36 calls per hour to calls per minute 36 1 hour hour 60 minutes calls per minute To find the mean number of calls per 5 minute interval multiply the mean number of calls per minute by 5 5 minutes mean number of calls per minute 5 Thus for a 5 minute time interval we have calls per 5 minutes and x

Find the limit est lim t 1 t9 t109 1

5 If the slope of the curve y f x at 1 9 is 6 f 9 Simplify your answer find f 9

Find the variation constant and an equation of variation where y varies inversely as x and y 7 when x 2 The variation constant is The equation of variation is y

3 Refer to the information below A and B are angles in standard position Without using a calculator find the exact value of sin A B sin A 3 5 sin B 12 13 0 A T B 3 2

8x 9x 1 a Find its inverse and check your answer b Find the domain and the range of f and f 1 The function f x is one to one OA The domain is x x Type integers or fractions Use a comma to separate answers as needed B The domain is xx 9 Type integers or fractions Use a comma to separate answers as needed OC The domain is x x Type integers or fractions Use a comma to separate answers as needed OD The domain is the set of all real numbers Find the range of f Select the correct choice below and if necessary fill in the answer box to complete your choice OA The range is yly Type integers or fractions Use a comma to separate answers as needed OB The range is yly Type integers or fractions Use a comma to separate answers as needed OC The range is ylys Type integers or fractions Use a comma to separate answers as needed D The range is the set of all real numbers S

The graph of a one to one function is shown to the right Draw the graph of the inverse function f 1 Choose the correct graph of the inverse function f OA OB below 5 O D E C

Use the figure to solve each inequality yo 5 1 0 4 2 1 g x 0 1 4 00 2 g x 0 1 5 5 4 0 2 X y g x

2 Use the following functions f x x 4 and g x x 2 to solve each of the following 5 f x 0 6 g x 0 7 f x g x

Find the indicated nth partial sum of the arithmetic sequence 3 12 21 30 n 25

Find the sum of the infinite geometric series if possible Round your answer to three decimal places If not possible enter IMPOSSIBLE 10 0 2 8 n 0

Question Graph the Logarithmic Function y log z by plotting the Horizontal Intercept and one other point Clear All Draw S 9 LOO 9 10

Find the coefficient a of the given term in the expansion of the binomial Binomial 4x 3y 8 a Term axyA

Find the specified nth term in the expansion of the binomial x 10z n 5

Use a graphing utility to find nCr 550C547

Find the sum of the infinite geometric series if possible Round your answer to three decimal places 7 0 55 STEP 1 Determine the first term of the infinite geometric series n o STEP 2 Find the common ratio of the infinite geometric series STEP 3 Based on your results from Step 1 and Step 2 the Sum of an Infinite Geometric Series Formula may be applied to this series What guarantees the formula will work in this The common ratio is less than the first term of the series The first term of the series is positive The first term of the series has an absolute value less than 1 O The common ratio has an absolute value less than the first term of the series The first term of the series has an absolute value greater than the common ratio The common ratio has an absolute value less than 1 The common ratio is less than one STEP 4 Compute the sum of the series using the Sum of an Infinite Geometric Series Formula Round your answer to three decimal places S

Find the rational number representation of the repeating decimal 0 945

llowing calculate the new temperature in degrees when pressure is changed with n and V constant A tank of helium gas with a pressure of 240 torr at 0 C is heated to give a pressure of 1400 torr Express your answer using two significant figures T Submit Part B AEO Request Answer C A sample of air at 45 0 C and 725 mmHg is cooled to give a pressure of 695 mmHg Express your answer using two significant figures VAE

the A swimming club can currently accommodate up to 100 members for a year long training program They plan to increase their pool capacity to accommodate up to an additional 75 members into the program every year To make a profit the club must have at least 50 members enrolled in the program The club manager expects the minimum membership requirement for making a profit to increase by 20 every year The manager modeled this situation with a system of inequalities where x is time from today in years and y is the number of members She graphed the system to show the solution region when the club is making a profit Number of Members 2 000 1 800 1 600 1 400 1 200 1 000 800 600 400 200 68 10 12 14 16 18 20 Time years What system of inequalities did the manager create 0 24

Solve the given equation for x 45x 2 2 32

a Approximate the area under graph a of f x 3 x over the interval 2 10 by computing the area of each rectangle to four decimal places and then adding b Approximate the area under graph b of f x 3 x over the interval 2 10 by computing the area of each rectangle to four decimal places and then adding Ay 0 75 0 375 C 0 Ay 0 75 0 375 2 0 4 4 f x 3 x CO 5 6 x 3 x 6 00 8 a 10 b 7 8 9 10 X O o The area under graph a is approximately Round to four decimal places as needed

A plane is 144 mi north and 186 mi east of an airport Find x the angle the pilot should turn in order to fly directly to the airport Round your answer to the nearest tenth of a degree W N 144 Airport 186 X E 0 X

HAD A A f x 2 x c 1 B f x c 1 C S x 2 c 4 D f x 2 x c 4 represents an f c for a function f x and a number c Find fand e The limit lim 40

Write the first five terms of the arithmetic sequence Use the table feature of a graphing utility to verify your results as 15 814 91 5 a 32 03 34 as

3 1 Points DETAILS LARPRECALCRMRP7 8 2 042 Write the first five terms of the arithmetic sequence Find the common difference and write the nth term of the sequence as a function of n a 3 5 ak 1 ak 3 5 12 93 34 as Common difference an Need Help Submit Answer Read It Watch t MY NOTES

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1 Let an converge to D 5n 3n 1 10n 11n 12 5x 3x XX Exam 3 Determine whether the sequence converges If so what does it 10x3 11x 2 5 3n 10 n 1 n

x 6x 5 X Z Hole vertical V A X 2 Y int 5 13 12 x 5 x 1 X 2 Asymptote 2 5 0 2 5 Horizontal Siant Asymptote y o X int 0 x s X 1 X 2 0 x 5 x 1 0 x S S X 5 0 0 XH 1 X 1 0 InstaGraphs 100 1 47 3 LIFT HERE 1 ILN E www instagraphs com 123456789

4 3 2 3 3 O 6 4 The graph of a function y f x is shown Make a sketch of the antiderivative F given that F is continuous and F 0 3 6 ont Det

2 x 5x16 x 4 x 2 x 3 xx2 x 2 Hole vertical A V A X2 y int oro 6 0 0 4 3 Z 1 S 0 1 5 Horizontal Slant Aysymptate x 45x SXt6 X int x 2 x 3 x x 2 0 x 2 x 3 0 X 2 2 X 3 x 2 0 3 0 0 x 3

6 Sketch a function for which each of the following conditions is satisfied lim f x 1 f 0 0 x x f x 0 for x 0 f x 0 for 1 x 1 f x 0 for x 0 f x 0 for x 1 and x 1

D D 3 D a State the domain b Determine the intervals of increase and decrease Increasing c Determine all local maximum and minimum points Local maximum d Determine the intervals of concavity Concave up e State any points of inflection Decreasing Local minimum Concave down YA

3x 3 Determine the equations of all asymptotes for the function f x 4x 7x 1 x 2x 1

2 Match each equation with the graph of the corresponding function below A y B y X x 3 4x x 9 C y D y x x 3 x 1 X 1 8 20 HITHTHITHI HH 2 4 6 8 HHH 4 2 11

2 Calculate go f and fog for the following f g a f x 2x 3 g x x 1 d f x g x x 2 g f x 1 x 1 g x x 4 b f x x c f x x 2x 1 1 g x 3x 5 g x f f x x 2 g x x 2 i f x x 1 g x x 3 e f x 2 x 1 g x x 4 h f x x 1 g x x 2x X

5 Consider the function Find all the points where f is continuous f x 1 if x Q 0 if x Q

f Determine if the function h x if x 0 0 if x 0 is continuous at x 0 if x 0 8 X

X 2 b Investigate the continuity of the function g x at x 2 c Check the continuity of the function h x x 3 at x 3

d Investigate the continuity of the function f x x 1 X 1 x if x 0 if 0 x 1 at if x 1

Given f x 7 x and g x 6x find the following expressions a fog 4 b gof 2 c fof 1 d gog 0 198 a fog 4 14 6 Type an exact answer using radicals as needed Simplify your answer b gof 2 Type an exact answer using radicals as needed Simplify your answer

For f x 8x and g x x find fog x and gof x Then determine whether fog x gof x What is fog x fog x ww

g x 3 2 4 x 1 2

ople there are at least two people who have the same birthday the same month and day of called the birthday problem is to find the probability that in a group of the year Assume a person is as likely to be born on one day as another

8 cos x 1 n 0 1 n x n 2n

Find the second degree Taylor polynomial for f x 5x 9x 2 about x 0 P x What do you notice about your polynomial

A woman deposits 11 000 at the end of each year for 6 years in an account paying 7 interest compounded annually a Find the final amount she will have on deposit b Her brother in law works in a bank that pays 6 compounded annually If she deposits money in this bank instead of the other one how much will she have in her account c How much would she lose over 6 years by using her brother in law s bank a She will have a total of on deposit Simplify your answer Round to the nearest cent as needed b She will have a total of on deposit in her brother in law s bank Simplify your answer Round to the nearest cent as needed c She would lose Simplify your answer over 6 years by using her brother in law s bank Round to the nearest cent as needed

A pharmacist has 80 milliliters of a 25 saline solution Which expression can be used to find the percentage concentration of the final solution if she adds x milliliters of a 10 saline solution y 0 25 80 0 1x 100